his observations might have been the result of standardizing the test scores... IE if you have a test that only scores 50 max and you scale it to 100 obviously you aren't going to have many odd numbers in the results.
He points out that in some of the tests all scores of 94-100 inclusive were obtained, so it's not a case of leaving out odds or a regularly-spaced set of numbers based on a simple scaling up/down.
If you have a maximum score of 53 you might chose a mapping function like this:
(rawscore 48) ? (rawscore * 2) : (rawscore + 47). That gives you a non-linear mapping with the slope cut in half for a small interval on the right side. The "can get steps of one and two" on the top mean nothing about what you can get below the knee when the mapping is non-linear.
Similar mappings can end up with both ends smooth and only the middle spiky.
Why do that? So you only get ONE discontinuity in the data, near the top, rather than one point of roundoff noising up the spacing and comparisons between students all through it.
A skewed distribution is hardly surprising, especially when the bulk of the measurements are near one end of a finite numbering system. Further, the non-linear mapping above would make the downslope on the right hand side shallower by a 2:1 ratio, exactly what you see. A distribution skewed toward the high end also argues for using a mapping like the one above - to spread out the pile of high-scoring students and make differences in score less divergent from differences in percentile rank.
The deficits just below passing scores and the spikes at them, however, are just bogus. The only "mapping" that can reasonably explain them is the "courtesy points" shoveling of just-failing students into just-passing. However, this can be explained as mercy being built into the mapping. (It can also be explained as protecting just-passing students from being unfairly pushed into the just-failing region due to a center-spreading, hump-flattening, non-linear mapping applied as a convenience for admissions officers.) The total absence of scores just below the fail point says it's not favoritism or individual corruption, but a systematic benefit given to all just-failing students.